U.S. patent application number 14/440264 was filed with the patent office on 2015-10-01 for device and method for estimating a flow of gas in an enclosure maintained at reduced pressure in relation to the gas.
This patent application is currently assigned to Commissariat a l'energie atomique et aux energies alternatives. The applicant listed for this patent is COMMISSARIAT L'ENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES. Invention is credited to Stephane Cros, Arnaud Leroy.
Application Number | 20150276443 14/440264 |
Document ID | / |
Family ID | 47989087 |
Filed Date | 2015-10-01 |
United States Patent
Application |
20150276443 |
Kind Code |
A1 |
Leroy; Arnaud ; et
al. |
October 1, 2015 |
DEVICE AND METHOD FOR ESTIMATING A FLOW OF GAS IN AN ENCLOSURE
MAINTAINED AT REDUCED PRESSURE IN RELATION TO THE GAS
Abstract
Method for estimating a gas flow in an enclosure maintained in a
low pressure regimen relative to the gas, including: measuring, as
a function of time, a gas flow J.sub.measurement in the enclosure,
and estimating values of the parameters A and B iteratively
implemented by decreasing an estimation error based on a difference
between J.sub.estim(t) and J.sub.measurement, and wherein, when
J.sub.measurement corresponds to a pressure rise of the gas in the
enclosure, J.sub.estim(t) is calculated according to the equation:
J estim ( t ) = 2 A n = 1 n ma x ( B .pi. ( t - OffX ) ) 1 2 exp (
- 2 ( n + 1 ) 2 4 B ( t - OffX ) ) + OffY ##EQU00001## and when
J.sub.measurement corresponds to a pressure decrease of the gas in
the enclosure, J.sub.estim(t) is calculated according to the
equation: J estm ( t ) = P init - 2 A n = 1 n ma x ( B .pi. ( t -
OffX ) ) 1 2 exp ( - ( 2 n + 1 ) 2 4 B ( t - OffX ) ) + OffY
##EQU00002##
Inventors: |
Leroy; Arnaud; (Chambery,
FR) ; Cros; Stephane; (Chambery, FR) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
COMMISSARIAT L'ENERGIE ATOMIQUE ET AUX ENERGIES
ALTERNATIVES |
Paris |
|
FR |
|
|
Assignee: |
Commissariat a l'energie atomique
et aux energies alternatives
Paris
FR
|
Family ID: |
47989087 |
Appl. No.: |
14/440264 |
Filed: |
November 6, 2013 |
PCT Filed: |
November 6, 2013 |
PCT NO: |
PCT/EP2013/073162 |
371 Date: |
May 1, 2015 |
Current U.S.
Class: |
702/47 |
Current CPC
Class: |
G01N 15/0826 20130101;
G01F 1/50 20130101 |
International
Class: |
G01F 1/50 20060101
G01F001/50 |
Foreign Application Data
Date |
Code |
Application Number |
Nov 6, 2012 |
FR |
12 60532 |
Claims
1. A method for estimating at least one gas flow in an enclosure
maintained in a low pressure regimen relative to the gas, including
at least: measuring, as a function of time, a gas flow
J.sub.measurement in the enclosure maintained in a low pressure
regimen relative to the gas, and estimating values of parameters A
and B iteratively implemented by decreasing an estimation error
based on a difference between an estimation of the gas flow
J.sub.estim(t) and the measured gas flow J.sub.measurement, and
wherein when the measured gas flow J.sub.measurement corresponds to
a pressure rise of the gas in the enclosure, the estimation of the
gas flow J.sub.estim(t) is calculated according to the equation: J
estim ( t ) = 2 A n = 1 n max ( B .pi. ( t - OffX ) ) 1 2 exp ( - (
2 n + 1 ) 2 4 B ( t - OffX ) ) + OffY ##EQU00034## and when the
measured gas flow J.sub.measurement corresponds to a pressure
decrease of the gas in the enclosure, the estimation of the gas
flow J.sub.estim(t) is calculated according to the equation: J
estim ( t ) = P init - 2 A n = 1 n max ( B .pi. ( t - OffX ) ) 1 2
exp ( - ( 2 n + 1 ) 2 4 B ( t - OffX ) ) + OffY ##EQU00035## with
OffX and OffY: relative integers; P.sub.init: initial value of a
measured partial pressure of the gas in the enclosure; n.sub.max:
integer higher than or equal to 1.
2. The method according to claim 1, wherein the gas is selected
from water vapor, oxygen, one of the water or oxygen isotopes,
helium, hydrogen, or a mixture of at least two of said gases.
3. The method according to claim 1, wherein estimating the values
of the parameters A and B includes at least the implementation of
the following steps of: a.sub.1) choosing initial values of the
parameters A and B; b.sub.1) calculating the estimation of the gas
flow J.sub.estim(t); c.sub.1) calculating the estimation error;
d.sub.1) when the estimation error is positive, decreasing the
value of the parameter A and/or the value of the parameter B, and
when the estimation error is negative, increasing the value of the
parameter A and/or the value of the parameter B; and wherein the
implementation of steps b.sub.1) to d.sub.1) is successively
repeated several times until a stabilization of the estimated
values of the parameters A and B is achieved.
4. The method according to claim 3, wherein step c.sub.1) includes
the implementation of the following steps of: dividing
J.sub.estim(t) and J.sub.measurement into several parts such that
each of these parts corresponds to J.sub.estim(t) and
J.sub.measurement for a time interval distinct from the time
intervals of the other parts; for each of the parts of
J.sub.estim(t) and J.sub.measurement, calculating a parameter
ErrorJ part_i = .intg. t .di-elect cons. part_i ( J estim ( t ) - J
measurement ) , ##EQU00036## with part_i corresponding to the time
interval of the corresponding parts of J.sub.estim(t) and
J.sub.measurement; calculating the parameters ErrorA and ErrorB,
corresponding to the estimation errors of the parameters A and B
respectively and forming together the estimation error, each of the
parameters ErrorA and ErrorB being equal to a linear combination of
the parameters ErrorJ.sub.part.sub.--.sub.i; and wherein step
d.sub.1) is implemented such that: when the value of the parameter
ErrorA is positive, the value of the parameter A is decreased; when
the value of the parameter ErrorA is negative, the value of the
parameter A is increased; when the value of the parameter ErrorB is
positive, the value of the parameter B is decreased; when the value
of the parameter ErrorB is negative, the value of the parameter B
is increased.
5. The method according to claim 3, wherein a stabilization of the
values of the parameters A and B is achieved when the values of the
parameters A and B include at least first six digits, in scientific
notation, identical to those of the values of the parameters A and
B obtained during a previous implementation of steps b.sub.1) to
d.sub.1).
6. The method according to claim 1, wherein the values of the
parameters A and B are decreased or increased by a variable pitch
the value of which depends on previous decreases or increases in
the values of the parameters A and B.
7. The method according to claim 1, wherein the estimation of the
values of the parameters A and B is implemented several times by
considering, at each of these estimations, different values of the
parameter OffX and/or the parameter OffY, and wherein final values
of the parameters A and B are chosen as being those for which a
global error between the measured gas flow J.sub.measurement and
the estimation of the gas flow J.sub.estim(t) is minimum among all
the steps of estimating the values of the parameters A and B
implemented.
8. The method according to claim 1, wherein, when a global error
between the measured gas flow J.sub.measurement and the estimation
of the gas flow J.sub.estim(t) reaches a minimum value at an
instant t.sub.x and is higher than this minimum value after
t.sub.x, a new estimation of values of parameters A.sub.x and
B.sub.x, corresponding to the parameters A and B for t>t.sub.x,
is implemented, wherein the values of the parameters A.sub.x and
B.sub.x are iteratively estimated by decreasing an estimation error
based on a difference, for t>t.sub.x, between an estimation of
the gas flow J.sub.estim.sub.--.sub.X(t) calculated based on the
estimated values of the parameters A.sub.x and B.sub.x and the
measured gas flow J.sub.measurement from which is subtracted the
estimation of the gas flow J.sub.estim(t) for t<t.sub.x, with X
an integer higher than 1, and wherein the previously calculated
parameters A and B are designated A.sub.1 and B.sub.1.
9. The method according to claim 1, wherein the enclosure
maintained in a low pressure regimen relative to the gas
corresponds to a second chamber of a permeameter which further
comprises a first chamber and a measurement device for measuring
the gas present in the second chamber, the first and second
chambers being separated from each other by a barrier layer having
a permeation toward the gas, and wherein the measured gas flow
J.sub.measurement is obtained from a measurement of the change over
time of the partial pressure of the gas in the second chamber.
10. The method according to claim 9, wherein, during the
implementation of the steps of measuring the gas flow
J.sub.measurement and estimating the values of the parameters A and
B, the barrier layer is saturated with gas, and wherein the
measured gas flow J.sub.measurement corresponds to a pressure
decrease of the gas in the second chamber of the permeameter.
11. The method according to claim 10, further including, after
estimating the values of the parameters A and B, calculating a
stabilized gas flow J.infin. such that J.infin.=AB or, when an
estimation of the values of the parameters A.sub.x and B.sub.x is
implemented, calculating stabilized gas flows J.infin..sub.x such
that J.infin..sub.X=A.sub.XB.sub.X.
12. A method for estimating a permeation of a barrier layer
relative to at least one gas, wherein the barrier layer separates a
first chamber from a second chamber of a permeameter, including at
least: depressurizing the first chamber and the second chamber
relative to the gas; firstly implementing a method for estimating a
gas flow according to claim 9 such that the measured gas flow,
designated J.sub.degas.sub.--.sub.measurement, corresponds to a
pressure decrease of the gas in the second chamber; calculating an
estimation of a gas flow J.sub.degas.sub.--.sub.estim(t) from the
last values of the parameters A and B previously estimated during
the first implementation of the method for estimating a gas flow;
introducing the gas into the first chamber such that the partial
pressure of the gas in the first chamber is higher than that in the
second chamber; secondly implementing a method for estimating a gas
flow according to claim 9 such that the measured gas flow
J.sub.measurement, corresponds to a pressure rise of the gas in the
second chamber, and during which the estimation of the values of
the parameters A and B is performed by decreasing the estimation
error based on a difference between an estimation of the gas flow
J.sub.perm.sub.--.sub.estim(t) and another gas flow
J.sub.perm.sub.--.sub.measurement such that
J.sub.perm.sub.--.sub.measurement=J.sub.measurement-J.sub.degas.sub.--.su-
b.estim(t).
13. The method according to claim 12, wherein, when a global error
between the measured gas flow J.sub.degas.sub.--.sub.measurement
and the estimation of the gas flow J.sub.degas.sub.--.sub.estim(t)
is lower than the value of a first threshold
Y.sub.lower.sub.--.sub.degas, the estimation of the gas flow
J.sub.degas.sub.--.sub.estim(t) is subtracted from the values of
the measured gas flow J.sub.measurement during the second
implementation of the method for estimating the gas flow and, when
the global error between the measured gas flow
J.sub.degas.sub.--.sub.measurement and the estimation
J.sub.degas.sub.--.sub.estim(t) is higher than the value of a
second threshold Y.sub.upper.sub.--.sub.degas, a last measured
value of the gas flow J.sub.degas.sub.--.sub.measurement or an
average of several last measured values of the gas flow
J.sub.degas.sub.--.sub.measurement is subtracted from the values of
the measured gas flow J.sub.measurement during the second
implementation of the method for estimating the gas flow.
14. The method according to claim 12, further including, after
estimating the values of the parameters A and B during the second
implementation of the method for estimating a gas flow, calculating
a stabilized gas flow J.infin. such that J.infin.=AB or, when an
estimation of the values of the parameters A.sub.x and B.sub.x is
implemented during the second implementation of a method for
estimating a gas flow, calculating stabilized gas flows
J.infin..sub.x such that J.infin..sub.X=A.sub.XB.sub.X.
15. A device for estimating a permeation of a barrier layer,
including means for implementing a method for estimating the
permeation of the barrier layer according to claim 1.
Description
TECHNICAL FIELD
[0001] The invention relates to a device and a method for
estimating at least one gas flow in an enclosure maintained in a
low pressure regimen relative to the gas(es). The invention is
applicable in particular for estimating the permeation, that is gas
barrier properties, of a barrier layer, or barrier film.
STATE OF PRIOR ART
[0002] Some devices, such as electronic components and photovoltaic
panels comprising organic materials, are particularly sensitive to
oxidation induced by water and dioxygen. In order to be able to
increase the lifetime of these devices, it is required to protect
them at the most by using barrier films, or barrier layers, having
strong water vapor and dioxygen barrier properties, for example
between about 10.sup.-3 gm.sup.-2day.sup.-1 and 10.sup.-6
gm.sup.-2day.sup.-1 for Water Vapor Transmission Rate (WVTR) and in
the order of 10.sup.-3 cm.sup.3m.sup.-2days.sup.-1 for Oxygen
Transmission Rate (OTR). Such barrier films are for example "Ultra
Barrier Solar Film" marketed by 3M.TM. Company, or X-Barrier.TM.
film marketed by Mitsubishi Plastics' Company.
[0003] The term "barrier" means here the protection provided by the
barrier material to the device with respect to the environment
gases responsible for the degradation of the device. The protection
of these atmosphere sensitive devices is all the more critical when
it should be made with flexible materials, a fortiori when they are
clear. The gas barrier properties of these layers of materials (or
barrier films) can vary a lot. The conventional barrier layers,
suitable for low demanding applications (for example in the food
field), have WVTR between about 10.sup.-1 and 1
gm.sup.-2days.sup.-1. The layers forming the strongest barriers to
the water vapor passage have WVTR lower than about 10.sup.-6
gm.sup.-2days.sup.-1. Thus, the barrier layers do not totally
prevent the gases from passing therethrough and thus have a
non-zero permeation relative to gases. It is thus important to be
able to measure their permeation level in order to ensure de
protection of devices protected with such barrier films.
[0004] The barrier properties of these barrier layers are measured
through the implementation of a permeation measurement of the
layers as schematically shown in FIG. 1, enabling the gas flow
transmitted by the barrier layer to be determined. A barrier layer
10 to be characterized is placed into a permeameter 11, at the
interface between a first chamber 12 and a second chamber 14 (see
FIG. 1, scheme a)). A measuring device 16 for detecting gases
present in the second chamber 14, by measuring in particular the
partial pressure of some isotopes of the gas as water vapor or
oxygen, is provided in the second chamber 14. This measuring device
16 corresponds for example to a mass spectrometer. The only
permeable wall between both chambers 12 and 14 is thus formed by
the barrier layer 10 the permeation of which is attempted to be
characterized. The first chamber 12 is filled with a target gas 18
at a controlled pressure, this gas 18 being able to be detected by
the measuring device 16.
[0005] The target gas 18 is for example water vapor or oxygen or
dioxygen, but the principle is true for any other gas or flavor
(see FIG. 1, scheme b)). The gas 18 present in the first chamber 12
is then transmitted into the second chamber 14 by a process of
solubility/diffusion through the barrier layer 10 (FIG. 1, scheme
c)). Such a permeameter 11 is for example described in document
U.S. Pat. No. 7,624,621 B2.
[0006] The performed permeation measurement of the barrier layer 10
gives a curve representing the change over time of the partial
pressure of the gas 18 in the second chamber 14, as shown in FIG.
2. In the case of an ideal flawless permeation regimen, that is
when the material of the barrier layer 10 is homogenous and the
diffusion coefficient of the barrier layer 10 does not vary as a
function of the target gas concentration during the measurement,
this curve, corresponding to the change over time of the transfer
rate of the gas 18 through the barrier layer 10, can be expressed
by the Fick equation:
J ( t ) = 2 P 1 S n = 1 .infin. ( D .pi. t ) 1 2 exp ( - ( 2 n + 1
) 2 l 2 4 Dt ) ( 1 ) ##EQU00003##
[0007] with P.sub.1: constant pressure of the gas 18 in the first
chamber 12;
[0008] S: solubility of the barrier layer 10;
[0009] D: Diffusion coefficient of the barrier layer 10;
[0010] I: thickness of the barrier layer 10.
[0011] A parameter C=P.sub.1S can also be used in the above
equation (1).
[0012] The curve given by the equation (1) above includes two
regimens: the first one, called a transient state regimen,
corresponds to the rise as a function of time in the flow of the
target gas 18 passing through the barrier layer 10. The second,
called a steady state regimen, expresses a constant flow of the
target gas 18 passing through the barrier layer 10 by
solubility/diffusion. The characteristic of the target gas flow to
be measured, that is the stabilized transfer rate, is obtained from
a steady state regimen of the measured flow curve and corresponds
to the constant value to which this curve tends. The stabilized
transfer rate of the gas 18 through the barrier layer 10 can be
expressed by the equation:
J .infin. = D S .DELTA. P l ( 2 ) ##EQU00004##
[0013] with .DELTA.P: partial pressure difference of the gas 18
between the first chamber 12 and the second chamber 14.
[0014] The stabilized transfer rate of the gas 18 through the
barrier layer 10 can also be approximated by the equation:
J .infin. = D C l ( 3 ) ##EQU00005##
[0015] When the target gas 18 is water vapor, this stabilized
transfer rate corresponds to WVTR, and when the target gas 18 is
oxygen or dioxygen, this rate corresponds to OTR.
[0016] From the analysis of the first and second regimens also
deduced is the characteristic time of the transient state regimen,
called "Time lag". This is calculated by integrating the transfer
rate curve of the gas 18 through the barrier layer 10, thus
representing the cumulative amount of the gas 18 that has passed
through the barrier layer 10, as a function of time. Such a curve
is shown in FIG. 3. The "Time lag" parameter is thus calculated by
extrapolating, at a zero amount, the linear change over time of the
cumulative amount of target gas 18 in the steady state regimen.
[0017] The permeation regimen can be more complex for barrier
materials including several layers such as inorganic deposits on a
polymeric substrate and/or in the case of a diffusion of a gas
strongly adsorbed by the barrier material (modification of the
diffusion coefficient over time). In this case, the change over
time of the rate transfer of such a complex permeation regimen can
be expressed by representative laws which are much more complex and
highly dependent on the materials being tested.
[0018] Furthermore, the implementation of such a permeation
measurement raises several problems.
[0019] First, as regards the sensitivity of the measurement
performed, the detection of the flow of the target gas 18
developing through the barrier layer 10 by the measuring device 16
is only possible if the signal to background noise ratio is in
accordance with the detection capabilities of the measuring device
16, that is if the value of the measured signal corresponding to
the gas flow 18 through the layer 10 is high enough to be distinct
from the background noise present in the second chamber 14. This
background noise comes from several factors: [0020] the minimum
electronic noise, or sensitivity of the measuring device 16, such
as the minimum ionization current detectable by a mass spectrometer
for the isotope of the target gas considered; [0021] the presence
of residual target gas in the second chamber 14 coming in
particular from the degassing from the walls of the second chamber
14 and from the layer 10 the permeation of which is attempted to be
measured (and also the filament of the mass spectrometer in the
case of a measurement by such an apparatus.
[0022] A second factor complexifying such a permeation measurement
is the measurement time sometimes necessary. Indeed, materials
having high barrier properties can include transient state regimens
(and thus "Time lags") which are particularly lengthy, that can
range up to several months.
[0023] Finally, a third factor complexifying the implementation of
such a measurement is the reliability of the measurement performed.
Indeed, the permanent flow characteristic of the target gas
measured, that is the transfer rate, can be readily truncated if
its reading is unintentionally performed in an anticipated way,
before the steady state regimen is reached.
[0024] These drawbacks are also found when a measurement of a gas
flow is desired to be performed in an enclosure maintained in a low
pressure regimen relative to the gas(es) to be measured, regardless
of whether this flow corresponds to a rise in pressure of the
target gas in the enclosure or to a decrease in the residual
pressure of the gas within the enclosure (corresponding for example
to a degassing in the enclosure, that is to the background
noise).
DISCLOSURE OF THE INVENTION
[0025] One purpose of the present invention is to provide a method
and a device allowing the change over time of one or several gas
flow(s) in an enclosure, or volume, maintained in a low pressure
regimen relative to the gas(es) measured, to be reliably simulated
and with a shortened time. One purpose of the present invention is
also to be able to perform an estimation of a permeation of a
barrier layer by making this measurement more sensitive, more
reliable and with a shortened time with respect to that necessary
to devices and methods of prior art for measuring a permeation for
estimating permeation properties of the barrier layer.
[0026] For this, the present invention provides a method for
estimating at least one gas flow in an enclosure maintained in a
low pressure regimen relative to the gas, including at least:
[0027] measuring, as a function of time, a gas flow
J.sub.measurement in the enclosure maintained in a low pressure
regimen relative to the gas, and [0028] estimating values of
parameters A and B iteratively implemented by decreasing an
estimation error based on a difference between an estimation of the
gas flow J.sub.estim(t) and the measured gas flow
J.sub.measurement,
[0029] and wherein when the measured gas flow J.sub.measurement
corresponds to a pressure rise of the gas in the enclosure, the
estimation of the gas flow J.sub.estim(t) is calculated according
to the equation:
J estim ( t ) = 2 A n = 1 n m ax ( B .pi. ( t - OffX ) ) 1 2 exp (
- ( 2 n + 1 ) 2 4 B ( t - OffX ) ) + OffY ##EQU00006##
[0030] and when the measured gas flow J.sub.measurement corresponds
to a pressure decrease of the gas in the enclosure, the estimation
of the gas flow J.sub.estim(t) is calculated according to the
equation:
J estim ( t ) = P init - 2 A n = 1 n max ( B .pi. ( t - OffX ) ) 1
2 exp ( - ( 2 n + 1 ) 2 4 B ( t - OffX ) ) + OffY ##EQU00007##
[0031] with OffX and OffY: relative integers;
[0032] P.sub.init: initial value of a measured partial pressure of
the gas in the enclosure;
[0033] n.sub.max: integer higher than or equal to 1.
[0034] The method according to the invention enables the gas flow
within the enclosure to be characterized without necessarily having
to wait for the steady state regimen of this flow to deduce
therefrom a value of the parameters A and B which enable this gas
flow to be characterized. Moreover, the estimation reliability of
this gas flow is improved because it is no longer possible to
unintentionally truncate the permanent flow characteristic of the
target gas being measured, that is the transfer rate, before the
steady state regimen is reached. The estimation of the values of
the parameters A and B is iteratively performed by approaching at
best the estimation J.sub.estim(t) of the measurement of the gas
flow performed for J.sub.measurement.
[0035] The gas flow is modeled by an equation expressing
J.sub.estim(t) and having properties similar to the Fick
equation.
[0036] When this method is applied to make an estimation of the
permeation of a barrier layer, the estimated parameters A and B can
in particular be used to calculate the diffusion coefficient and/or
solubility and/or transfer rate and/or Time Lag of the barrier
layer.
[0037] Because the enclosure is maintained in a low pressure
regimen relative to the gas, this low pressure regimen is thus
maintained permanently (dynamic system) and the change over time of
the partial pressure of the target gas within the enclosure thus
corresponds to a balance between the system making this low
pressure regimen, such as a pumping system (for example through the
use of a vacuum pump or a neutral gas flow) and the target gas flow
of the enclosure. The pumping ability can thus be considered as
constant whatever the partial pressure of target gas. Thus, the
change over time of the partial pressure can be considered as being
that of the target gas flow. This can be checked for insofar as the
system making the low pressure regimen, such as the pumping system,
is stabilized and the change over time of the partial pressure of
target gas is unlikely to alter the pumping speed. For example, in
the case of the use of a pumping system of the target gas through
vacuum, this can be checked if the nominal operating speed of the
pump is met and the pressure in the enclosure does not exceed about
10.sup.-5 mbar.
[0038] The flows can be expressed in cm.sup.3day.sup.-1 for gases
(or in gramday.sup.-1 for water). In the case where the expressed
flow is that of a permeation measurement, the flow value can be
normed by the film area measured (for example in
cm.sup.3day.sup.-1m.sup.-2).
[0039] The gas may be selected from water vapor, oxygen, dioxygen,
one of water or oxygen isotopes, helium, hydrogen, or a mixture of
at least two of said gases.
[0040] Estimating the values of the parameters A and B may include
at least the implementation of the following steps of:
[0041] a.sub.1) choosing initial values of the parameters A and
B;
[0042] b.sub.1) calculating the estimation of the gas flow
J.sub.estim(t);
[0043] c.sub.1) calculating the estimation error;
[0044] d.sub.1) when the estimation error is positive, decreasing
the value of the parameter A and/or the value of the parameter B,
and when the estimation error is negative, increasing the value of
the parameter A and/or the value of the parameter B;
[0045] and wherein the implementation of steps b.sub.1) to d.sub.1)
is successively repeated several times until a stabilization of the
estimated values of the parameters A and B is achieved.
[0046] Step c.sub.1) may include the implementation of the
following steps of: [0047] dividing J.sub.estim(t) and
J.sub.measurement into several parts such that each of these parts
corresponds to J.sub.estim(t) and J.sub.measurement for a time
interval distinct from the time intervals of the other parts;
[0048] for each of the parts of J.sub.estim(t) and
J.sub.measurement, calculating a parameter
[0048] ErrorJ part_i = .intg. t .di-elect cons. part_i ( J estim (
t ) - J measurement ) , ##EQU00008##
with part_i corresponding to the time interval of the corresponding
parts of J.sub.estim(t) and J.sub.measurement; [0049] calculating
the parameters ErrorA and ErrorB, corresponding to the estimation
errors of the parameters A and B respectively and forming together
the estimation error, each of the parameters ErrorA and ErrorB
being equal to a linear combination of the parameters
ErrorJ.sub.part.sub.--.sub.i;
[0050] and wherein step d.sub.1) is implemented such that: [0051]
when the value of the parameter ErrorA is positive, the value of
the parameter A is decreased; [0052] when the value of the
parameter ErrorA is negative, the value of the parameter A is
increased; [0053] when the value of the parameter ErrorB is
positive, the value of the parameter B is decreased; [0054] when
the value of the parameter ErrorB is negative, the value of the
parameter B is increased.
[0055] In this case, some parts of the curves of the gas flow
measured and of the estimation of the gas flow which are only
relevant for one of the parameters A and B may not be taken into
account for the estimation of the other of the parameters A and
B.
[0056] A stabilization of the values of the parameters A and B may
be achieved when the values of the parameters A and B include at
least first six digits, in scientific notation, identical to those
of the values of the parameters A and B obtained during a previous
implementation of steps b.sub.1) to d.sub.1).
[0057] The values of the parameters A and B may be decreased or
increased by a variable pitch the value of which depends on
previous decreases or increases of the values of the parameters A
and B. Thus, it is possible to shorten the time of implementation
of the method to obtain estimations of the values of the parameters
A and B.
[0058] The estimation of the values of the parameters A and B may
be implemented several times by considering, at each of these
estimations, different values of the parameter OffX and/or the
parameter OffY, and wherein final values of the parameters A and B
are chosen as being those for which a global error between the
measured gas flow J.sub.measurement and the estimation of the gas
flow J.sub.estim(t) is minimum among all the steps of estimating
the values of the parameters A and B implemented. An offset can
thus be readily corrected, in X (abscissa) and/or in Y (ordinate)
between the curve representing the estimation of the gas flow and
the curve representing the gas flow measured.
[0059] When a global error between the measured gas flow
J.sub.measurement and the estimation of the gas flow J.sub.estim(t)
reaches a minimum value at an instant t.sub.x and is higher than
this minimum value after t.sub.x (for example at least 10% higher
during at least 5% of the measurement time), a new estimation of
values of parameters A.sub.x and B.sub.x, corresponding to the
parameters A and B for t>t.sub.x, is implemented, wherein the
values of the parameters A.sub.x and B.sub.x are iteratively
estimated by decreasing an estimation error based on a difference,
for t>t.sub.x, between an estimation of the gas flow
J.sub.estim.sub.--.sub.X(t) calculated based on the estimated
values of the parameters A.sub.x and B.sub.x and the measured gas
flow J.sub.measurement from which is subtracted the estimation of
the gas flow J.sub.estim (t) for t<t.sub.x, with X an integer
higher than 1, and wherein the previously calculated parameters A
and B are designated A.sub.1 and B.sub.1.
[0060] The estimation of the values of the parameters A and B may
be implemented several times, which enables complex permeation
regimens to be described in a universal manner without resorting to
particular models for each material. A population of parameters (A;
B) is thus determined.
[0061] The enclosure maintained in a low pressure regimen relative
to the gas may correspond to a second chamber of a permeameter
which further comprises a first chamber and a measurement device
for measuring the gas present in the second chamber, the first and
second chambers being separated from each other by a barrier layer
having a permeation relative to the gas, and wherein the measured
gas flow J.sub.measurement is obtained from a measurement of the
change over time of the partial pressure of the gas in the second
chamber. The permeation measurement performed may correspond to the
measurement of WVTR or OTR of the barrier layer.
[0062] It is possible to determine the gas flow J.sub.measurement
measured from the measurement of the partial pressure and technical
characteristics of the permeameter.
[0063] For example, when the measuring device is a mass
spectrometer, the knowledge of the relationship between the
ionization current of the spectrometer and the partial pressure of
the target gas, or a calibration of the relationship target gas
partial pressure/target gas flow, enables the measurement of the
gas flow to be determined.
[0064] During the implementation of the steps of measuring the gas
flow J.sub.measurement and estimating the values of the parameters
A and B, the barrier layer may be saturated with gas, and the
measured gas flow J.sub.measurement may correspond to a pressure
decrease of the gas in the second chamber of the permeameter.
[0065] The method may further include, after estimating the values
of the parameters A and B, calculating a stabilized gas flow
J.infin. such that J.infin.=AB or, when an estimation of the values
of the parameters A.sub.x and B.sub.x is implemented, calculating
stabilized gas flows J.infin..sub.x such that
J.infin..sub.X=A.sub.XB.sub.X. A total stabilized gas flow may be
calculated and correspond to the sum of J.infin. and of
J.infin..sub.X.
[0066] The invention also relates to a method for estimating a
permeation of a barrier layer relative to at least one gas, wherein
the barrier layer separates a first chamber from a second chamber
of a permeameter, including at least: [0067] depressurizing the
first chamber and the second chamber relative to the gas; [0068]
firstly implementing a method for estimating a gas flow as
previously described, such that the measured gas flow, designated
J.sub.degas.sub.--.sub.measurement corresponds to a pressure
decrease of the gas in the second chamber; [0069] calculating an
estimation of a gas flow J.sub.degas.sub.--.sub.estim(t) from the
last values of the parameters A and B previously estimated during
the first implementation of the method for estimating a gas flow;
[0070] introducing the gas into the first chamber such that the
partial pressure of the gas in the first chamber is higher than
that in the second chamber; [0071] secondly implementing a method
for estimating a gas flow such as previously described such that
the measured gas flow J.sub.measurement, corresponds to a pressure
rise of the gas in the second chamber, and during which the
estimation of the values of the parameters A and B is performed by
decreasing the estimation error based on a difference between an
estimation of the gas flow J.sub.perm.sub.--.sub.estim(t) and
another gas flow J.sub.perm.sub.--.sub.measurement such that
J.sub.perm.sub.--.sub.measurement=J.sub.measurement-J.sub.degas.sub.--.su-
b.estim(t). This method allows in this case, from the parameters A
and B estimated during an estimation of the background noise in the
second chamber (corresponding to J.sub.degas.sub.--.sub.estim(t)),
the permeation of the barrier layer to be directly estimated from
these parameters.
[0072] Thus, this method enables the change over time of the
background noise to be efficiently simulated before performing the
permeation measurement of the barrier layer. Indeed, during the
first implementation of the method for estimating the gas flow,
this gas flow corresponds to a measurement of a background noise in
the second chamber (corresponding to the gas flows from the walls
of the second chamber, from the different degassings of the
measuring device as well as from the degassing of the barrier
layer). During the second implementation of the method for
estimating the gas flow, the measured gas flow J.sub.measurement
thus corresponds to the sum of the flows from the background noise
J.sub.degas.sub.--.sub.estim, that is the degassings occurring in
the second chamber, and the flow from the gas permeation through
the barrier layer J.sub.perm.sub.--.sub.measurement. By subtracting
the estimation of the gas flow J.sub.degas.sub.--.sub.estim(t) from
the measured gas flow J.sub.measurement during the estimation of
the parameters A and B, the measurement sensitivity of the gas flow
corresponding to the permeation through the barrier layer is thus
dramatically improved.
[0073] When a population of parameters (A; B) is determined, that
is when the gas diffusion mechanism through the barrier layer is
complex, for example in the case of a barrier layer including
defects and/or having a diffusion coefficient varying as a function
of the target gas concentration in the material, the method
according to the invention enables the principles of the Fick
equation to be applied to such complex diffusion regimens which are
conventionally known not to meet the Fick's law. It is thus
possible to apply the estimation method to barrier layers the
permeation of which does not follow a model governed by a single
permeation regimen (corresponding to a single Fick equation) but
follows a model corresponding to a sum of several permeation
regimens different from each other, each being able to be modeled
using an equation derived from the Fick equation and the parameters
A and B of which are distinct from those of other permeation
regimens. In the same way, the estimation of the parameters A and B
may be implemented several times in order to best describe
J.sub.degas.sub.--.sub.estim(t).
[0074] When a global error between the measured gas flow
J.sub.degas.sub.--.sub.measurement and the estimation of the gas
flow J.sub.degas.sub.--.sub.estim(t) is lower than the value of a
first threshold Y.sub.lower.sub.--.sub.degas, the estimation of the
gas flow J.sub.degas.sub.--.sub.estim(t) is subtracted from the
values of the gas flow J.sub.perm.sub.--.sub.measurement measured
during the second implementation of the method for estimating the
gas flow and, when the global error between the measured gas flow
J.sub.degas.sub.--.sub.measurement and the estimation
J.sub.degas.sub.--.sub.estim(t) is higher than the value of a
second threshold Y.sub.upper.sub.--.sub.degas, a last measured
value of the gas flow J.sub.degas.sub.--.sub.measurement or an
average of several last measured values of the gas flow
J.sub.degas.sub.--.sub.measurement is subtracted from the values of
the gas flow J.sub.perm.sub.--.sub.measurement(t) measured during
the second implementation of the method for estimating the gas
flow.
[0075] The method may further include, after estimating the values
of the parameters A and B during the second implementation of the
method for estimating a gas flow, calculating a stabilized gas flow
J.infin. such that J.infin.=AB or, when an estimation of values of
parameters A.sub.x and B.sub.x is implemented during the second
implementation of a method for estimating a gas flow, calculating
stabilized gas flows J.infin..sub.x such that
J.infin..sub.X=A.sub.XB.sub.X. A total stabilized gas flow may be
calculated and then correspond to the sum of J.infin. and
J.infin..sub.X.
[0076] The invention also relates to a device for estimating a
permeation of a barrier layer, including means for implementing a
method for estimating the permeation of the barrier layer as
previously described.
[0077] There is also provided a method for estimating a permeation
of a barrier layer relative to at least one gas, including at least
one measurement, as a function of time, of a gas flow
J.sub.measurement passing through the barrier layer through
permeation, and an estimation of the values of parameters D and S,
corresponding to a diffusion coefficient and a solubility of the
barrier layer respectively, wherein the values of the parameters D
and S are iteratively estimated by reducing a first estimation
error based on a difference between an estimation of the gas flow
J.sub.estim(t) calculated based on the estimated values of the
parameters D and S and the measured gas flow J.sub.measurement.
BRIEF DESCRIPTION OF THE DRAWINGS
[0078] The present invention will be better understood upon reading
the description of exemplary embodiments given by way of purely
indicating and in no way limiting purposes making reference to the
appended drawings wherein:
[0079] FIG. 1 shows a device and a method for measuring a
permeation of a barrier layer;
[0080] FIGS. 2 and 3 show measurement curves of the change over
time of a gas partial pressure and a cumulative gas amount as a
function of time through a barrier layer;
[0081] FIG. 4 shows different steps of a method for estimating the
permeation of a barrier layer, object of the present invention,
according to a particular embodiment;
[0082] FIG. 5 shows the steps implemented for estimating a
background noise in the measurement enclosure of a permeameter
during a method for estimating the permeation of a barrier layer,
object of the present invention, according to a particular
embodiment;
[0083] FIG. 6 shows curves corresponding to the measured background
noise and the estimated background noise during a method for
estimating the permeation of a barrier layer, object of the present
invention, according to a particular embodiment;
[0084] FIG. 7 shows the steps implemented for estimating the
parameters D and S during a method for estimating the permeation of
a barrier layer, object of the present invention, according to a
particular embodiment;
[0085] FIGS. 8 to 10 show curves corresponding to the measured gas
flow and the estimated gas flow during a method for estimating the
permeation of a barrier layer, object of the present invention,
according to a particular embodiment;
[0086] FIG. 11 shows the change over time of a global error between
an estimated gas flow and a measured gas flow when this gas flow is
governed by several permeation regimens;
[0087] FIG. 12 shows a device for measuring a permeation, object of
the present invention, according to a particular embodiment.
[0088] Identical, similar or equivalent parts of the different
figures described hereinafter bear the same reference numerals so
as to facilitate switching from one figure to the other.
[0089] Different parts shown in the figures are not necessarily
drawn at a uniform scale, for the figures to be more legible.
[0090] The different possibilities (alternatives and embodiments)
should be understood as being non-exclusive from each other and can
be combined between them.
DETAILED DISCLOSURE OF PARTICULAR EMBODIMENTS
[0091] The implementation of a method for estimating the permeation
of a barrier layer 10, or barrier film, having in particular
barrier properties relative to one or more gases is described
according to a particular embodiment. The gas(es) considered here
is (are) for example water vapor, dioxygen, one of the water or
oxygen isotopes, helium, hydrogen or a mixture of at least two of
these gases. This method is implemented using in particular a
permeameter 11 as previously described in connection with FIG. 1.
The different steps of this method are shown in FIG. 4 as a
diagram.
[0092] A first step of this method is to calculate an estimation of
the change over time of the background noise in the detection
enclosure of the permeameter 11, that is in the second chamber 14
of the permeameter 11 (step 102). This estimation of the background
noise is to estimate the change over time of the gas flow in the
enclosure formed by the second chamber 14 and which corresponds to
a pressure decrease of the gas in the enclosure. Indeed, the
degassing of the walls of the second chamber 14 and of the barrier
layer 10 to be characterized is gradually decreasing and varies
over time from the moment when the second chamber 14 is maintained
in a low pressure regimen relative to the target gas, corresponding
for example to vacuumizing the second chamber 14. The estimation of
the change over time of the background noise, referred to as
J.sub.degas.sub.--.sub.estim, will thus allow, during the
subsequent measurement and estimation of the gas permeation through
the barrier layer 10, the component of the background noise to be
known in the gas flow transmitted through the barrier layer 10
which will be measured, referred to as
J.sub.perm.sub.--.sub.measurement, and thus in the estimation of
this gas flow, referred to as J.sub.perm.sub.--.sub.estim(t).
[0093] For estimating J.sub.degas.sub.--.sub.estim, the barrier
layer 10 to be characterized is provided at the interface between
the first chamber 12 and the second chamber 14 of the permeameter
11, as shown in scheme a) of FIG. 1.
[0094] The chambers 12 and 14 are placed in a low pressure of the
gas(es) considered.
[0095] This estimation of J.sub.degas.sub.--.sub.estim is performed
from measurements of the background noise, called
J.sub.degas.sub.--.sub.measurement. In parallel to the measurement
of J.sub.degas.sub.--.sub.measurement, calculations are thus
performed to estimate J.sub.degas.sub.--.sub.estim. These
calculations are iteratively performed by attempting to be as close
as possible to the estimation J.sub.degas.sub.--.sub.estim of the
measurement J.sub.degas.sub.--.sub.measurement.
[0096] The background noise related to the degassing in the second
chamber 14 of the permeameter 11 can correspond to a degassing
curve obeying a slightly modified Fick equation. Indeed, the
unmodified Fick equation describes an upflow, corresponding to the
flow of the gas 18 passing through the barrier layer 10, and
corresponds to the previously indicated equation (1). The degassing
curve corresponding to the background noise is a flow decreasing
with time which is expressed by the following equation (3):
J degas ( t ) = P init - 2 C n = 1 .infin. ( D .pi. t ) 1 2 exp ( -
( 2 n + 1 ) 2 l 2 4 D t ) ( 4 ) ##EQU00009##
[0097] with I: constant;
[0098] P.sub.init: initial value of a partial pressure of the gas
18 in the second chamber 14;
[0099] C: parameter proportional to the solubility S of the barrier
layer 10;
[0100] D: diffusion coefficient of the barrier layer 10.
[0101] In order to dispense with the constant I, the above equation
(4) can be written as:
J degas ( t ) = P init - 2 A n = 1 .infin. ( B .pi. t ) 1 2 exp ( -
( 2 n + 1 ) 2 l 2 4 B t ) ( 5 ) ##EQU00010##
[0102] with A and B: natural numbers such that A=C.times.I and
B=D/I.sup.2.
[0103] The steps implemented for estimating the background noise
102 are shown in the diagram of FIG. 5.
[0104] First, initial values of the parameters A and B which will
be used to calculate the estimation of the background noise (step
102.1) are defined. These initial values of the parameters A and B
are for example arbitrarily chosen by the user, and correspond for
example to values close to those expected and empirically
known.
[0105] A vacuum, for example lower than 10.sup.-6 mbar, is made in
the first chamber 12 and the second chamber 14. Then measurements
of a background noise J.sub.degas.sub.--.sub.measurement are
performed, by the measuring device 16, in the second chamber 14
(step 102.2) corresponding to the degassing of the gas in the
second chamber 14, this degassing being triggered by vacuumizing
the second chamber 14. The parameters of this measurement depend in
particular on the water load, the composition and structure of the
barrier layer 10. The duration for implementing this measurement
can range from a few minutes to several days or weeks if the
barrier layer 10 and/or the second chamber 14 are strongly polluted
by water. It is for example possible to measure
J.sub.degas.sub.--.sub.measurement at a frequency of a measuring
point every two seconds, or a higher frequency if the measuring
device 16 permits it.
[0106] In step 102.3, a calculation of an estimation of
J.sub.degas.sub.--.sub.estim(t) is then performed according to the
equation:
J degas_estim ( t ) = P init - 2 A n = 1 n max ( B .pi. t ) 1 2 exp
( - ( 2 n + 1 ) 2 l 2 4 B t ) ( 6 ) ##EQU00011##
[0107] The P.sub.init value is for example chosen as being the
first measured value of J.sub.degas.sub.--.sub.measurement. It
corresponds to the initial partial pressure of the gas considered
in the second chamber 14 and is lower than the vacuum level
initially made. For example, as soon as the water loaded barrier
layer 10 is placed in contact with the vacuum, the barrier will
begin to degas. Therefore, there will no longer be as a high vacuum
as that obtained without the loaded barrier layer. The n.sub.max
value is for example chosen as being higher than or equal to 1, for
example equal to 30. Switching from step 102.2 to 102.3 is made
when there are at least two measuring points, that is at least two
values of J.sub.degas.sub.--.sub.measurement.
[0108] Then, an estimation error of J.sub.degas.sub.--.sub.estim is
calculated based on a difference between
J.sub.degas.sub.--.sub.estim(t) and
J.sub.degas.sub.--.sub.measurement (step 102.4). Unlike the
measured background noise J.sub.degas.sub.--.sub.measurement which
corresponds to a finite number of measuring points obtained on a
finite duration (corresponding to the duration until which the
measurement is performed), the estimated background noise
J.sub.degas.sub.--.sub.estim(t) can be calculated on any duration
because it is expressed as a mathematical function. To make the
calculation of the estimation error of
J.sub.degas.sub.--.sub.estim(t), the function
J.sub.degas.sub.--.sub.estim(t) is considered on a range of values
of t corresponding to the duration of the measurement of
J.sub.degas.sub.--.sub.measurement previously made. A comparison of
both curves corresponding to J.sub.degas.sub.--.sub.measurement and
J.sub.degas.sub.--.sub.estim(t) can thus be made on a same time
interval.
[0109] Because of the specificities of the Fick equation (1) which
are also applied to the preceding equations (4) to (6) modeling the
change over time of the background noise, the parameter A can be
considered as only varying the amplitude of the curve corresponding
to J.sub.degas.sub.--.sub.estim(t), whereas B can be considered as
varying the "spread" of this curve along the time axis. Given that
the degassing corresponding to the background noise is always
decreasing, the estimation error of the value of the parameter A
can be obtained by considering the end of the measurement and
estimation curves of the background noise, whereas that of the B
value can be visible with little interference of A at the start of
the measurement and estimation curves of the background noise.
[0110] In order to be able to calculate independently the
estimation errors of the parameters A and B, the curves
corresponding to J.sub.degas.sub.--.sub.estim(t) and
J.sub.degas-measurement will be divided into several parts along
the time axis. For each of these parts, an error parameter is
calculated such that:
ErrorJ degas_part _i = .intg. t .di-elect cons. part_i ( J
degas_estim ( t ) - J degas_measurement ) ( 7 ) ##EQU00012##
[0111] with part_i corresponding to the time interval of the parts
corresponding to J.sub.degas.sub.--.sub.estim(t) and
J.sub.degas-measurement. The calculation of thus integral is
performed by considering the measuring points of
J.sub.degas.sub.--.sub.measurement obtained on the time interval
corresponding to the considered part of the curves, the values of
J.sub.degas.sub.--.sub.estim(t) being calculated for different
values of t corresponding to the instants at which the measuring
points of J.sub.degas.sub.--.sub.measurement have been
obtained.
[0112] The error of each of these parts corresponds to the area
lying between the measurement and estimation curves at each of
these parts.
[0113] The error is positive when this area is above the
measurement curve (in the case of an overestimation of the
background noise), and negative when this area is below the
measurement curve (in the case of an underestimation of the
background noise).
[0114] These different integrals are then combined between them to
calculate estimation errors of the parameters A and B.
[0115] A first possibility to calculate the estimation errors of
the parameters A and B can be to consider the measurement and
estimation curves of the background noise as being each formed by
two distinct parts by "intersecting" the time axis into two. In the
example of FIG. 6, the curve 50 represents the measured background
noise J.sub.degas.sub.--.sub.measurement and includes a first part
50.1 for t .epsilon.[0; t.sub.1] and a second part 50.2 for t
.epsilon.[t.sub.1; t.sub.2]. The curve 52 represents the estimation
of the background noise J.sub.degas.sub.--.sub.estim(t) and
includes a first part 52.1 for t .epsilon.[0; t.sub.1] and a second
part 52.2 for t .epsilon.[t.sub.1; t.sub.2]. t.sub.1 and t.sub.2
values are for example such that t.sub.2 is equal to about twice
t.sub.1, the interval [0; t.sub.2] corresponding for example to the
total duration during which the background noise has been measured.
The estimation error on each of both parts is then calculated
according to the above equation (7), by calculating the integral of
the difference between the estimation and the measurement of the
background noise. The errors of the parameters A and B are then
calculated such that:
ErrorB = .intg. t .di-elect cons. [ 0 ; t 1 ] ( J degas_estim ( t )
- J degas_measurement ) = ErrorJ degas_part _ 1 ( 8 ) ErrorB =
.intg. t .di-elect cons. [ t 1 ; t 2 ] ( J degas_estim ( t ) - J
degas_measurement ) = ErrorJ degas_part _ 2 ( 9 ) ##EQU00013##
[0116] A second possibility to calculate ErrorA and ErrorB can be
to consider the measurement and estimation curves as being each
formed by four distinct parts: a first part of each of both curves
on an interval t.epsilon.[0; t.sub.1], a second part of each of
both curves on an interval t .epsilon.[t.sub.1; t.sub.2], a third
part of each of the curves on an interval t.epsilon.[t.sub.2;
t.sub.3], a fourth part of each of the curves on an interval
t.epsilon.[t.sub.3; t.sub.4]. Here, t.sub.4 corresponds to the end
of the measurement of the background noise, and these four parts
each span around one quarter of this total duration. The error on
each of these four parts is then calculated according to the above
equation (7), by calculating the integral of the difference between
the estimation and the measurement of the background noise. The
errors of the parameters A and B are then calculated by combining
the different errors calculated for the different parts of the
curves such that for example:
ErrorB = .intg. t .di-elect cons. [ 0 ; t 1 ] ( J degas_estim ( t )
- J degas_measurement ) + 2 .intg. t .di-elect cons. [ t 1 ; t 2 ]
( J degas_estim ( t ) - J degas_measurement ) + 3 .intg. t
.di-elect cons. [ t 2 ; t 3 ] ( J degas_estim ( t ) - J
degas_measurement ) ( 10 ) ErrorA = 2 .intg. t .di-elect cons. [ t
3 ; t 4 ] ( J degas_estim ( t ) - J degas_measurement ) + .intg. t
.di-elect cons. [ t 2 ; t 3 ] ( J degas_estim ( t ) - J
degas_measurement ) ( 11 ) ##EQU00014##
[0117] There is thus in this case:
ErrorB=ErrorJ.sub.degas.sub.--.sub.part.sub.--.sub.1+2ErrorJ.sub.degas.s-
ub.--.sub.part.sub.--.sub.2+3ErrorJ.sub.degas.sub.--.sub.part.sub.--.sub.3-
, and
ErrorA=2ErrorJ.sub.degas.sub.--.sub.part.sub.--.sub.4+ErrorJ.sub.degas.s-
ub.--.sub.part.sub.--.sub.3.
[0118] A third possibility to calculate the estimation errors of
the parameters A and B can be to consider the measurement and
estimation curves as being each formed by four distinct parts: a
first part of each of both curves on an interval
t.epsilon.[t.sub.1; t.sub.2], a second part of each of both curves
in an interval t.epsilon.[t.sub.2; t.sub.3], a third part of each
of the curves on an interval t.epsilon.[t.sub.3; t.sub.4], and a
fourth part of each of the curves on an interval
t.epsilon.[t.sub.4; t.sub.5]. Here, t.sub.5 corresponds to the end
of the measurement of the background noise and t.sub.1 corresponds
to the t value for example from which the values of
J.sub.degas.sub.--.sub.measurement are lower than the sum of the
first measured value of J.sub.degas.sub.--.sub.measurement and
twice the standard deviation of the first 30 measured values of
J.sub.degas.sub.--.sub.measurement. The time intervals of these
four parts correspond to durations approximately equal to each
other. The error of each of these four parts is then calculated as
set out above according to the equation (7), by calculating the
integral of the difference between the estimation and the
measurement of the background noise.
[0119] The errors of the parameters A and B are then calculated by
combining the different errors calculated for the different parts
of the curves such as for example:
ErrorB = .intg. t .di-elect cons. [ t 1 ; t 2 ] ( J degas_estim ( t
) - J degas_measurement ) + 2 .intg. t .di-elect cons. [ t 2 ; t 3
] ( J degas_estim ( t ) - J degas_measurement ) + 3 .intg. t
.di-elect cons. [ t 3 ; t 4 ] ( J degas_estim ( t ) - J
degas_measurement ) ( 12 ) ErrorA = 2 .intg. t .di-elect cons. [ t
4 ; t 5 ] ( J degas_estim ( t ) - J degas_measurement ) + .intg. t
.di-elect cons. [ t 3 ; t 4 ] ( J degas_estim ( t ) - J
degas_measurement ) ( 13 ) ##EQU00015##
[0120] The three calculation possibilities of the errors of the
parameters A and B set out above are exemplary embodiments, and
other linear combinations of the errors of the different parts of
the measurement and estimation curves of the background noise can
be made for calculating ErrorA and ErrorB. It is also possible to
take parts of the curves partly overlapping with each other into
account.
[0121] Once the calculations of the estimation errors of the
parameters A and B are made, the values of the parameters A and B
are modified by adding to or subtracting from them a respective
"pitch", as a function of the value, and in particular of the sign,
of the estimation error of the parameter (step 102.5). If the error
of the parameter (ErrorA or ErrorB) is negative, this means that
the estimated value of the parameter is too small, and thus that
the estimated value of the corresponding parameter should be
increased. Conversely, if the error of the parameter is positive,
this means that the estimated value of the parameter is too high
and thus that the estimated value of the parameter should be
decreased. The pitch value of each parameter is for example between
about 110.sup.-25 and 110.sup.-6.
[0122] In step 102.6, a stabilization of the estimation of the
background noise is then assessed by analyzing the variation in the
estimations of the parameters A and B with respect to the previous
estimation (when this is the first estimation of the parameters A
and B, steps 102.2 to 102.6 are automatically repeated). Indeed, if
the values of these parameters are stabilized, this means that the
model selected for the estimation (thus the values of A and B) does
correspond to the measurement and thus that the estimation made of
the background noise is stable. It is considered for example that
the values of the parameters A and B are stabilized when the values
of these parameters include at least first six digits, in
scientific notation, identical to those of the values of these
parameters obtained during a previous estimation. If the values of
the parameters A and B are not stabilized, steps 102.2 to 102.6 are
repeated until a stabilization of these parameters is achieved.
[0123] When the values of the parameters A and B are considered as
being stable, the estimation of the background noise
J.sub.degas.sub.--.sub.estim(t) obtained from these estimated
values of A and B is globally compared with
J.sub.degas.sub.--.sub.measurement in order to determine whether
this estimation is satisfactory (step 102.7). In order to quantify
the accuracy of this estimation, the latter can be defined as being
the reverse of a global error between the estimated background
noise J.sub.degas.sub.--.sub.estim(t) and the measurement of the
background noise J.sub.degas.sub.--.sub.measurement. Thus, the
lower the calculating global error, the more accurate the
estimation of the background noise. This global error can for
example be defined as being the sum relating to each point of the
squared difference between the measurement and the estimation such
that:
ErrGlobJ degas = 1 p i = 1 p ( J degas_measurement ( i ) - J
degas_estim ( i ) ) 2 ( 14 ) ##EQU00016##
[0124] with p corresponding to the number of points taken into
account, for example equal to the number of measuring points of the
background noise.
[0125] It is possible to reduce the offset influence along the axis
Y of the measurement (offset on the axis of the pressure value) at
the beginning of the measurement by calculating the global error
according to the equation:
ErrGlobJ degas = 1 p - a i = 1 p ( J degas_measurement ( i ) - J
degas_estim ( i ) ) 2 ( 15 ) ##EQU00017##
[0126] with a representing the start of the decrease of the signal
J.sub.degas.sub.--.sub.measurement, for example the point from
which the value of the measuring signal
J.sub.degas.sub.--.sub.measurement is lower than the average of the
first measuring points minus twice the associated standard
deviation on a sufficiently long duration, for example on about 10
measuring points.
[0127] The measurement and estimation of the background noise can
be made in connection with the sensitivity desired by the operator
for the measurement. The device used for the implementation of this
method can in particular permanently indicate the sensitivity of
the measuring apparatus at the time t by applying for example a
multiplicative factor of 100 with respect to the estimated
background noise.
[0128] This global error is for example calculated at the end of 10
minutes of measurement, with a duration for example lower than
about 1 week.
[0129] If the matching between the estimation and the measurement
of the background noise is considered as insufficient, that is the
global error calculated above is higher than a threshold
Y.sub.upper.sub.--.sub.degas for example equal to about 15%, the
operator can however start the measurement of the gas flow through
the barrier layer to be characterized. The sensitivity indicated
can be considered such that there is a ratio of 1/100 between the
background noise measured at the time of starting the measurement
and the measurement sensitivity wanted by the operator. It is also
possible that the sensitivity corresponds to about 1/100 of an
average of the last measuring points of the background noise
corresponding for example to about 20% of the measurement if the
stabilization is achieved.
[0130] A fixed value corresponding to the background noise (last
measured value of the background noise or average of the last
measured values of the background noise) will be subtracted from
the permeation measurement performed thereafter (step 102.8).
[0131] The operator can also discontinue the estimation of the
background noise at any time if he/she considers that the
sensitivity corresponding to the minimum detection threshold of a
stabilized value with respect to the background noise obtained at
that time is sufficient for the measurement.
[0132] If the matching between the simulation and measurement of
the background noise is considered as sufficient, that is if the
calculated global error is lower than a threshold
Y.sub.lower.sub.--.sub.degas, for example equal to 5%, the
indicated sensitivity then considers the scattering of the
measuring points of J.sub.degas.sub.--.sub.measurement about the
curve of J.sub.degas.sub.--.sub.estim(t). Indeed, in this case, the
measuring points of the degassing represent a Gaussian about an
average represented by the simulated point (for the time
considered). This scattering is characterized by its standard
deviation. The deviation between the simulation curve of the
degassing and the measured points enables the measurement curve to
be obtained. Thus, a prolonged deviation (for example in the order
of a few tens seconds, or one or several minutes) higher than twice
the standard deviation will correspond to the signal from the
sample and will thus not be attributable to a degassing phenomenon.
The estimation curve J.sub.degas-estim(t) could be subtracted from
the permeation measurement performed thereafter (step 102.9).
[0133] For each of these possibilities, an automatic start of the
measurement of the gas flow can be programmed. The operator then
simply indicates the desired sensitivity for the measurement. The
measurement procedure automatically starts as soon as the
conditions desired by the user are met, that is when the
measurement sensitivity wanted by the operator is higher than twice
the standard deviation.
[0134] If the matching between the estimation and the measurement
of the background noise is not considered as sufficient, that is if
the global error indicated above is between
Y.sub.upper.sub.--.sub.degas and Y.sub.lower.sub.--.sub.degas, it
is then possible to consider that the change over time of the
background noise follows a first equation
J.sub.degas.sub.--.sub.estim.sub.--.sub.1 (t), based on the values
of the parameters A and B calculated and referred to as A.sub.1 and
B.sub.1, on a first range of values of t, and that this background
noise also follows one or several other equations
J.sub.degas.sub.--.sub.estim.sub.--.sub.X(t) adding to the first
equation J.sub.degas.sub.--.sub.estim.sub.--.sub.1 (t), based on
parameters A.sub.x and B.sub.x different from A.sub.1 and B.sub.1,
on one or several other ranges of values of t, with X an integer
higher than 1.
[0135] Indeed, a background noise, or more generally a degassing,
can include several regimens each corresponding to a Fick model
(corresponding to the equation (5) above) governed by its own
parameters A and B. In this case, the model of the change over time
of the background noise can be expressed by the equation:
J degas_estim _total ( t ) = i = 1 m J degas_estim _i ( t ) ( 16 )
##EQU00018##
[0136] where m is the number of degassing regimens corresponding to
the background noise.
[0137] These m degassing regimens are added up. It should then be
determined when the degassing regimen changes such that a new
regime has to be added to
J.sub.degas.sub.--.sub.estim.sub.--.sub.total(t). This moment is
determined by the follow-up of the global error previously
calculated. In order to best determine the sum of several degassing
regimens, the global error previously described can be defined by
the following equation:
ErrGlobJ degas = 1 p i = 1 p J degas_measurement ( i ) - J
degas_estim ( i ) J degas_measurement ( i ) ( 17 ) ##EQU00019##
[0138] To be able to obtain the parameters A and B of all the
degassing regimens, the parameters of the first degassing regimen,
referred to as J.sub.degas.sub.--.sub.1, are set when the error
begins to increase. It is then possible to subtract the first
degassing regimen from the measurement to make appear a new signal
only depending on the next degassing regimen(s)
J.sub.degas.sub.--.sub.x, with X an integer higher than 1. This
signal could thus be processed in the same way as the measurement
to extract the other degassing regimens therefrom.
[0139] The determination of A.sub.1 and B.sub.1, enabling
J.sub.degas.sub.--.sub.1 to be determined, uses the estimated data
just before the global error increases by more than 30% of the
point considered during a long enough duration (1H30 for example,
or more in the case of strong barrier properties, as one day or
more). Steps 102.2 to 102.6 are implemented only from these data
until stabilized values of A.sub.1 and B.sub.1 are obtained.
[0140] In the present case, steps similar to steps 102.1 to 102.6
can be implemented (iteratively as previously described) by
subtracting the preceding degassing regimen(s) from the measurement
to extract and determine the following degassing regimens.
[0141] Each of the degassing regimens is governed by its own
equation (corresponding to the preceding equation (5)) and thus
includes its own parameters A and B characterizing the degassing
occurring in the period of the degassing regimen considered.
[0142] In step 102.5, it is possible to vary A and B for example at
a constant pitch as previously described, or at a variable value
pitch, that is a value multiplied by a coefficient unique to each
parameter and the value of which can change according to the change
over time of the error on the parameters A and B. Thus, this
coefficient will be for example divided by 2 if the parameter
oscillates between two values, which allows to gain in accuracy on
the estimated parameter. In the same way, the coefficient will be
for example increased by about 10% if the parameter changes several
times at a stretch in the same direction, which enables the
estimation quickness to be improved, when the values of the
estimated parameters A and B are too far from the final values.
[0143] For example, at each iteration of step 102.5, the value of B
can be modified by adding or subtracting a pitch .DELTA.B and/or
the value of A can be modified by adding or subtracting a pitch
.DELTA.A such that: [0144] if B changes twice at a stretch in the
same direction, .DELTA.B can for example be increased by 10%.
[0145] if A changes twice at a stretch in the same direction,
.DELTA.A can for example be increased by 10%.
[0146] Example for A: [0147] estimation 1 with A(1); [0148] if
ErrorA positive, then estimation 2 with A(2)=(A1)-.DELTA.A; [0149]
if ErrorA still positive, then .DELTA.A=.DELTA.A.times.1.1, and
estimation 3 with A(3)=A(2)-.DELTA.A; [0150] if B and/or A
oscillates about the same value (example: B(i)=B(i-2) and/or
A(i)=A(i-2)), .DELTA.A and/or .DELTA.B can be divided by 2.
[0151] Example: [0152] estimation 1 with B(1) and/or A(1); [0153]
if ErrorB and/or ErrorA positive, then estimation 2 with
B(2)=B(1)-.DELTA.B and/or A(2)=A(1)-.DELTA.A; [0154] if ErrorB
and/or ErrorA negative, then estimation 3 with
B(3)=B(2)+.DELTA.B=B(1) and/or A(3)=A(2)+.DELTA.A=A(1), and
.DELTA.B=.DELTA.B/2 and/or .DELTA.A=AA/2; [0155] in the other
cases, .DELTA.B and .DELTA.A can remain constant.
[0156] There is no limit in the number of measuring points of the
background noise that can be used to achieve the estimation of the
background noise. However, in order to reduce the calculation load,
it is possible to average the measuring signal about a maximum
number of points (for example 2000).
[0157] Thus, during step 102, the change over time of the
background noise is estimated thanks to the estimation of the
values of the parameters A and B which enable
J.sub.degas.sub.--.sub.estim(t) to be deduced therefrom. In the
embodiment described herein, the estimated values of the parameters
A and B obtained during the estimation of the background noise are
not used to directly deduce therefrom the stabilized transfer rate
J.infin. of the barrier layer 10.
[0158] The measurement of the gas flow 18 through the barrier layer
10 is then performed (step 104). The second chamber 14 being
already under vacuum, the first chamber 12 of the permeameter 11 is
then filled by the gas(es) 18 the permeation of which through the
barrier layer 10 is desired to be measured. This measured flow,
referred to as J.sub.measurement, will be used to estimate the
change over time of the gas flow related to the permeation (step
106), and it will then be possible to estimate the stabilized
transfer rate expressed by the above equation (2) as well as
possibly the Time lag of the barrier layer 10 (step 108).
[0159] The gas flow 18 measured through the barrier layer 10, which
is directly proportional to the measurement of the partial pressure
of the gas(es) in the second chamber 14, is governed by the Fick
equation, corresponding to the previously mentioned equation (1).
The gas flow corresponding to the permeation through the barrier
layer 10 can thus be expressed by the equation:
J perm ( t ) = 2 C n = 1 .infin. ( D .pi. t ) 1 2 exp ( - ( 2 n + 1
) 2 l 2 4 D t ) ( 18 ) ##EQU00020##
[0160] with I: thickness of the layer of material.
[0161] Analogously with the previously described equation (6) for
the estimation of the background noise, the gas flow corresponding
to the permeation through the barrier layer 10 can thus be
expressed by the equation:
J perm_estim ( t ) = 2 A n = 1 n max ( B .pi. t ) 1 2 exp ( - ( 2 n
+ 1 ) 2 4 B t ) ( 19 ) ##EQU00021##
[0162] with n.sub.max: integer higher than or equal to 1, for
example equal to 30.
[0163] As for the estimation of the previously described change
over time of the background noise, the estimation of the change
over time of the gas flow is iteratively determined by attempting
to be as close as possible to the measurement estimation.
[0164] The steps implemented to calculate the estimation of the gas
flow J.sub.perm.sub.--.sub.estim(t) are shown in the diagram of the
FIG. 7.
[0165] First, initial values of the parameters A and B are defined,
which will be used to calculate the estimation
J.sub.perm.sub.--.sub.estim(t) (step 106.1). These initial values
of the parameters A and B are for example arbitrarily chosen by the
user.
[0166] In step 106.2, a calculation of an estimation of the gas
flow J.sub.perm.sub.--.sub.estim(t) is then performed according to
the equation (19) above.
[0167] Then, an estimation error of the gas flow is calculated
based on a difference between the estimation of the flow
J.sub.perm.sub.--.sub.estim(t) and the values of the measurements
of the flow J.sub.perm.sub.--.sub.measurement(t) which corresponds
to the measured flow J.sub.measurement minus the previously
estimated background noise J.sub.degas.sub.--.sub.estim(t) (step
106.3). This estimation error will be calculated in a substantially
analogous way to the previously calculated estimation error of the
background noise.
[0168] Unlike the measured flow J.sub.measurement, and thus also
unlike J.sub.perm.sub.--.sub.measurement, which corresponds to a
finite number of measuring points obtained on a finite duration
(corresponding to the duration until which the measurement is
performed), the estimated gas flow J.sub.perm.sub.--.sub.estim(t)
can be calculated on any duration because the estimated gas flow is
expressed as a mathematical function. To perform the calculation of
the estimation error of the gas flow, the function
J.sub.perm.sub.--.sub.estim(t) is considered on a range of values
of t corresponding to the duration of the measurement of the gas
flow performed. A comparison of both curves corresponding to
J.sub.perm.sub.--.sub.measurement(t) and
J.sub.perm.sub.--.sub.estim(t) can thus be performed on a same time
interval.
[0169] As previously described for the background noise, because of
the specificities of the Fick equation, the parameter A can be
considered as varying only the amplitude of the estimation
J.sub.perm.sub.--.sub.estim(t), whereas B can be considered as
varying the "spread" of the curve along the time axis.
[0170] Different parts of J.sub.perm.sub.--.sub.measurement and
J.sub.perm.sub.--.sub.estim(t) are considered to independently
determine the estimation errors of the parameters A and B.
[0171] In order to be able to independently calculate the
estimation errors of the parameters A and B,
J.sub.perm.sub.--.sub.estim(t) and
J.sub.perm.sub.--.sub.measurement are divided into several parts
along the time axis. For each of these parts, an error parameter is
calculated such that:
ErrorJ perm_part _i = .intg. t .di-elect cons. part_i ( J
perm_estim ( t ) - J perm_measurement ) ( 20 ) ##EQU00022##
[0172] with part_i corresponding to the time interval of the
corresponding parts of J.sub.perm.sub.--.sub.estim(t) and
J.sub.perm.sub.--.sub.measurement. The calculation of this integral
is performed by considering the measuring points of
J.sub.perm.sub.--.sub.measurement which are obtained on the time
interval corresponding to the considered part of the curves, the
values of J.sub.perm.sub.--.sub.estim(t) being calculated for
different values of t corresponding to the corresponding instants
of the measuring points of J.sub.perm.sub.--.sub.measurement.
[0173] The error of each of these parts corresponds to the area
located between the measurement and estimation curves at these
parts. The error is positive when this area is above the
measurement curve, and negative when this area is below the
measurement curve. These different integrals are combined to each
other to calculate the estimation errors of the parameters A and
B.
[0174] As previously described for the estimation of the background
noise, a first alternative to calculate the estimation errors of
the parameters A and B can be to consider the measurement and
estimation curves of the flow gas as being each formed by two
distinct parts by "intersecting" the time axis into two. In the
example of FIG. 8, the curve 60 represents the measured gas flow
J.sub.perm.sub.--.sub.measurement and includes a first part 60.1
for t.epsilon.[0; t.sub.1] and a second part 60.2 for
t.epsilon.[t.sub.1; t.sub.2]. The values of t.sub.1 and t.sub.2 can
be different from those previously described to determine the
estimation error of the background noise. Curve 62 represents the
estimation of the gas flow J.sub.perm.sub.--.sub.estim(t) and
includes a first part 62.1 for t.epsilon.[0; t.sub.1] and a second
part 62.2 for t.epsilon.[t.sub.1; t.sub.2]. The values of t.sub.1
and t.sub.2 are for example such that t.sub.2 is equal to about
twice t.sub.1, the interval [0; t.sub.2] corresponding to the total
duration during which the gas flow has been measured. The
estimation error of each of both these parts is then calculated
according to the equation (15) above, by calculating the integral
of the difference between the estimation and the measurement of the
gas flow. The errors of the parameters A and B are then calculated
such that:
ErrorB = .intg. t .di-elect cons. [ 0 ; t 1 ] ( J perm_estim ( t )
- J perm_measurement ) = ErreurJ perm_part _ 1 ( 21 ) ErrorA =
.intg. t .di-elect cons. [ t 1 ; t 2 ] ( J perm_estim ( t ) - J
perm_measurement ) = ErreurJ perm_parti 2 ( 22 ) ##EQU00023##
[0175] Analogously to the previously estimated background noise, a
second alternative to calculate the estimation errors of the
parameters A and B can be to consider the measurement and
estimation curves as being each formed by four distinct parts, as
shown in FIG. 9: a first part 60.1 and 62.1 of each of both curves
on an interval t .epsilon.[0; t.sub.1], a second part 60.2 and 62.2
of each of both curves on an interval t .epsilon.[t.sub.1;
t.sub.2], a third part 60.3 and 62.3 of each of the curves on an
interval t.epsilon.[t.sub.2; t.sub.3], and a fourth part 60.4 and
62.4 of each of the curves on an interval t.epsilon.[t.sub.3;
t.sub.4]. Here, t.sub.4 corresponds to the end of the measurement
of the gas flow, and these four parts each span about a quarter of
this total duration. The error on each of these four parts is then
calculated according to the equation (20) above, by calculating the
integral of the difference between the estimation and the
measurement of the gas flow. The errors of the parameters A and B
are then calculated by combining the different errors calculated
for the different parts of the curves such as for example:
ErrorB = .intg. t .di-elect cons. [ 0 ; t 1 ] ( J perm_estim ( t )
- J perm_measurement ) + 2 .intg. t .di-elect cons. [ t 1 ; t 2 ] (
J perm_estim ( t ) - J perm_measurement ) + 3 .intg. t .di-elect
cons. [ t 2 ; t 3 ] ( J perm_estim ( t ) - J perm_measurement ) (
23 ) ErrorA = 2 .intg. t .di-elect cons. [ t 3 ; t 4 ] ( J
perm_estim ( t ) - J perm_measurement ) + .intg. t .di-elect cons.
[ t 2 ; t 3 ] ( J perm_estim ( t ) - J perm_measurement ) ( 24 )
##EQU00024##
[0176] There is thus
ErrorB=ErrorJ.sub.perm.sub.--.sub.part.sub.--.sub.1+2ErrorJ.sub.perm.sub-
.--.sub.part.sub.--.sub.2+3ErrorJ.sub.perm.sub.--.sub.part.sub.--.sub.3,
and
ErrorA=2ErrorJ.sub.perm.sub.--.sub.part.sub.--.sub.4+ErrorJ.sub.perm.sub-
.--.sub.part.sub.--.sub.3.
[0177] In comparison with the first alternative previously set out
consisting in separating the curves into two parts, a division into
four parts of the measurement and estimation curves to calculate
the estimation errors of the parameters A and B allows to obtain
finally a lower global estimation error in particular when the
measurement layer has a slight X offset, that is an offset on the
time axis, with respect to the theoretical model.
[0178] A third alternative to calculate the estimation errors of
the parameters A and B can be to consider the measurement and
estimation curves as being each formed by four distinct parts as
shown in FIG. 10: a first part 60.1 and 62.1 of each of both curves
on an interval t.epsilon.[t.sub.1; t.sub.2], a second part 60.2 and
62.2 of each of both curves on an interval t.epsilon.[t.sub.2;
t.sub.3], a third part 60.3 and 62.3 of each of the curves on an
interval t.epsilon.[t.sub.3; t.sub.4], and a fourth part 60.4 and
62.4 of each of the curves on an interval t.epsilon.[t.sub.4;
t.sub.5]. Here, t.sub.5 corresponds to the end of the measurement
of the gas flow and t.sub.1 corresponds for example to the value
oft from which the values of J.sub.perm.sub.--.sub.measurement are
lower than the sum of the first measured value of
J.sub.perm.sub.--.sub.measurement and twice the standard deviation
of the first 30 measured values of
J.sub.perm.sub.--.sub.measurement. The time intervals of these four
parts correspond to durations approximately equal to each other.
The error of each of these four parts is then calculated as set out
above according to the equation (20), by calculating the integral
of the difference between the estimation and the measurement of the
gas flow. The errors of the parameters A and B are then calculated
by combining the different errors calculated for the different
parts of the curves such as for example:
ErrorB = .intg. t .di-elect cons. [ t 1 ; t 2 ] ( J perm_estim ( t
) - J perm_measurement ) + 2 .intg. t .di-elect cons. [ t 2 ; t 3 ]
( J perm_estim ( t ) - J perm_measurement ) + 3 .intg. t .di-elect
cons. [ t 3 ; t 4 ] ( J perm_estim ( t ) - J perm_measurement ) (
25 ) ErrorA = 2 .intg. t .di-elect cons. [ t 4 ; t 5 ] ( J
perm_estim ( t ) - J perm_measurement ) + .intg. t .di-elect cons.
[ t 3 ; t 4 ] ( J perm_estim ( t ) - J perm_measurement ) ( 26 )
##EQU00025##
[0179] In comparison with the first two alternatives previously
described, this third alternative for calculating estimation errors
of the parameters A and B is more versatile and is more suitable
even when the measurement signal diverges from the theoretical Fick
model.
[0180] The three alternatives for calculating the errors of the
parameters A and B are exemplary embodiments, and other linear
combinations of the errors of the different parts of the
measurement and estimation curves of the gas flow can be made to
calculate ErrorA and ErrorB. As for the estimation of the
background noise, it is possible to consider parts of the curves
partly overlapping with each other.
[0181] Once these error calculations are carried out, the values of
the parameters A and B are modified by adding to or subtracting
from them their respective "pitch" as a function of the value of
the estimation error of the parameter (step 106.4). If the error of
the parameter (ErrorA or ErrorB) is negative, this means that the
estimated value of the parameter is too small, and thus that the
estimated value of the corresponding parameter has to be increased.
Conversely, if the error of the parameter is positive, this means
that the estimated value of the parameter is too great and thus
that the estimated value of the parameter should be decreased. The
pitch value of each parameter is for example between about
110.sup.-25 and 110.sup.-6.
[0182] In step 106.5, the stabilization of the values of the
parameters A and B is then assessed by analyzing the variation of
the parameters A and B with respect to the previous estimation.
Indeed, if the values of these parameters are stabilized, this
means that the model chosen does correspond to the measurement and
that the estimation performed of the gas flow is then reliable. It
is considered for example that the values of the parameters A and B
are stabilized when the values of these parameters include at least
first six digits, in scientific notation, identical to those of the
values of these parameters obtained during a previous estimation.
If the values of the parameters A and B are not stabilized, steps
106.2 to 106.5 are repeated until a stabilization of these
parameters is achieved. In parallel to this repetition of these
steps, the measurement of the gas flow (step 104) is continued in
order to continue to take the last measuring points of the gas flow
into account in the estimation of the gas flow.
[0183] When the values of the parameters A and B are considered as
being stable, the estimation of the gas flow
J.sub.perm.sub.--.sub.estim(t) obtained from the estimated values
of A and B is globally compared with
J.sub.perm.sub.--.sub.measurement in order to determine whether
this estimation is satisfactory (step 106.6). In order to quantify
the accuracy of this estimation, the latter can be defined as being
the reverse of a global error between the estimated gas flow
J.sub.perm.sub.--.sub.estim(t) and the measurement of the gas flow
J.sub.perm.sub.--.sub.measurement. Thus, the lower the calculated
global error, the more accurate the estimation of the gas flow.
This global error can be defined as being the sum related to each
point of the squared difference between the measurement and the
estimation such that:
ErrGlobJ perm = 1 p i = 1 p ( J perm_measurement ( i ) - J
perm_estim ( i ) ) 2 ( 27 ) ##EQU00026##
[0184] with p corresponding to the number of points taken into
account, for example equal to the number of measuring points of the
gas flow.
[0185] It is possible to decrease the influence of the offset along
the axis Y of the measurement (offset on the axis of the pressure
value) at start of the measurement by calculating the global error
according to the equation:
ErrGlobJ perm = 1 p - a i = a p ( J perm_measurement ( i ) - J
perm_estim ( i ) ) 2 ( 28 ) ##EQU00027##
[0186] with a representing the start of the increase of the signal
J.sub.perm.sub.--.sub.measurement, for example the point from which
the value of the measurement signal
J.sub.perm.sub.--.sub.measurement exceeds the average of the first
measuring points summed to the associated standard deviation, for
example on about 10 measuring points.
[0187] The device used for implementing this method can
continuously display the estimated values of the parameters A, B,
the global error parameter as well as the value of the stabilized
flow and Time lag which are estimated based the estimated values of
A and B, calculated based on the equations (29) and (30) indicated
later.
[0188] If the matching between the simulation and the measurement
of the gas flow is considered as sufficient, that is if the
previously calculated global error is lower than a threshold
Y.sub.perm, for example between 0 and 5%, the end of the
measurement of the gas flow can be anticipated, the estimated
values of the parameters A and B being then considered as right.
From the previously estimated parameters, the permeation of the
barrier layer 10 can thus be assessed (step 108) by calculating for
example the value of the stabilized gas flow J.infin. such
that:
J.infin.=AB (29)
[0189] and/or the parameter TL (Time lag) such that:
TL = B 6 . ( 30 ) ##EQU00028##
[0190] Besides the J.infin. and TL values, it is possible to
calculate the values of D (diffusion coefficient) and S
(solubility) of the barrier layer from the estimated values of A
and B, in accordance with the previously described equations.
[0191] If the matching between the estimation and the measurement
of the gas flow is not considered as sufficient, that is if the
global error indicated above is higher than a threshold Y.sub.perm,
it is then possible to consider that the gas flow follows a first
equation J.sub.perm.sub.--.sub.estim.sub.--.sub.1 (t), based on the
values of the parameters A and B calculated and referred to as
A.sub.1 and B.sub.1, on a first range of values of t, and that this
gas flow also follows one or more other equations
J.sub.perm.sub.--.sub.estim.sub.--.sub.X(t) adding up to the first
equation J.sub.perm.sub.--.sub.estim.sub.--.sub.1(t), based on the
parameters A.sub.x and B.sub.x different from A.sub.1 and B.sub.1,
on a second range of values oft.
[0192] Indeed, some barrier layers can include several permeation
regimens each corresponding to a Fick model governed by its own
parameters A and B. In this case, the model of the gas flow through
the barrier layer can be expressed by the equation:
J perm_estim _total ( t ) = i = 1 m J perm_estim _i ( t ) ( 31 )
##EQU00029##
[0193] where m is then the number of permeation regimens of the
barrier layer.
[0194] These m permeation regimens are added up. Therefore, it
should be determined when the permeation regimen changes such that
a new regimen has to be added to
J.sub.perm.sub.--.sub.estim.sub.--.sub.total(t). This moment is
determined by following the previously calculated global error. In
order to best determine the sum of several permeation regimens, the
previously described global error can be defined by the following
equation:
ErrGlobJ perm = 1 p i = 1 p J perm_measurement ( i ) - J perm_estim
( i ) J perm_measurement ( i ) ( 28 ) ##EQU00030##
[0195] FIG. 11 shows an exemplary change over time of the
calculated global error by considering that the gas flow is
governed by a single Fick equation whereas the actual permeation
regimen of the barrier layer consists of the sum of several
distinct permeation regimens. It can be seen in this figure that
the global error is stable up to about the 20 000.sup.th second,
and then the global error increases. This is due to the fact that
the influence of a new permeation regimen is actual at that time
and is added up to the first permeation regimen.
[0196] To be able to obtain the parameters A and B of all the
permeation regimens, the parameters of the first permeation
regimen, referred to as J.sub.perm.sub.--.sub.1, are set when the
error starts to increase. It is thus possible to subtract the first
permeation regimen from the measurement to make appear a new signal
only depending on the next permeation regimen(s)
J.sub.perm.sub.--.sub.x, with X an integer higher than 1. This
signal could thus be processed in the same way as the measurement
to extract the other permeation regimens therefrom.
[0197] The determination of A.sub.1 and B.sub.1, enabling
J.sub.perm.sub.--.sub.1 to be determined, uses the estimated data
just before the global error increases by more than 30% of the
considered point for a sufficiently long duration (1H30 for
example, or more in the case of strong barrier properties, as one
day or more). Steps 106.2 to 106.5 are only implemented from these
data until stabilized values of A.sub.1 and B.sub.1 are
obtained.
[0198] Because in step 106.6, the global error parameter is higher
than the threshold Y.sub.perm, step 106.7 is then implemented and
consists in implementing steps similar to steps 106.2 to 106.5
(iteratively as previously described) by subtracting the permeation
regimen(s) from the measurement to extract and determine the next
permeation regimens.
[0199] Thus, according to an exemplary gas flow curve according to
several permeation regimens, it is possible to have a first
permeation regimen J.sub.perm.sub.--.sub.1 the influence of which
starts as soon as the measurement begins, a second permeation
regimen J.sub.perm.sub.--.sub.2 the influence of which starts from
the 20 000.sup.th second, a third permeation regimen
J.sub.perm.sub.--.sub.3 the influence of which starts from the 30
000.sup.th second, and a fourth permeation regimen
J.sub.perm.sub.--.sub.4 the influence of which here starts from the
50 000.sup.th second. Each of the permeation regimens is governed
by its own Fick equation and thus includes its own parameters A and
B characterizing the gas flow in the period of the permeation
regimen considered.
[0200] When several permeation regimens are taken into
consideration, step 108 then consists in calculating, from the
previously described equations 24 and 25, a value of a stabilized
flow J.infin. and of TL for each permeation regimen.
[0201] In previously described step 106.4, it is possible to vary A
and B for example according to a constant pitch, or a variable
pitch, that is a value multiplied by a coefficient unique to each
parameter and the value of which can change according to the change
over time of the error on parameters A and B.
[0202] Thus, this coefficient will be for example divided by 2 if
the parameter oscillates between two values, which allows a gain in
accuracy on the estimated parameter. In the same way, the
coefficient will be for example increased by about 10% if the
parameter changes several times at a stretch in the same direction,
which enables the quickness of the estimation start to be improved,
when the estimated parameters A and B are too far from their final
values.
[0203] For example, at each iteration of step 106.4 for the
permeation regimen to be estimated, the value of B can be modified
by adding or subtracting a pitch .DELTA.B and the value of A can be
modified by adding or subtracting a pitch .DELTA.A such that:
[0204] if B changes two times at a stretch in the same direction,
.DELTA.B can for example be increased by 10%. [0205] If A changes
two times at a stretch in the same direction, .DELTA.A can for
example be increased by 10%. [0206] if B and/or A oscillates about
the same value, .DELTA.A and/or .DELTA.B can be divided by 2.
[0207] In the other cases, .DELTA.B and .DELTA.A can remain
constant.
[0208] There is no limit in the number of measuring points of the
gas flow that can be used. However, in order to reduce the
calculation load, it is also possible to average a too long
measuring signal about a maximum number of points (for example 2
000).
[0209] It can happen that the X (time axis) and Y (axis of the
pressure measured) offsets, respectively called OffX and OffY, have
an importance such that the best estimation of the gas flow
corresponds to the measurement of the gas flow, and this as much
for the background noise as for the permeation. To obtain the
couple (offset X, offset Y) giving the lowest global error, steps
106.1 to 106.5 for the permeation and/or steps 102.1 to 102.6 for
the background noise can be repeated by offsetting at each time the
curve corresponding to the measurement of the gas flow of a low
unit along the time axis (for example 1 second), this loop being
included in another loop making such an offset of the measurement
of the gas flow along the ordinate axis (for example by 110.sup.-15
Pa).
[0210] In this case, the estimation of the permeation can be
expressed by the following equation:
J perm_estim ( t ) = 2 A n = 1 n max ( B .pi. ( t - OffX ) ) 1 2
exp ( - ( 2 n + 1 ) 2 4 B ( t - OffX ) ) + OffY ( 33 )
##EQU00031##
[0211] The estimation of the background noise can be expressed by
the following equation:
J deg as_estim ( t ) = P init - 2 A n = 1 n max ( B .pi. ( t - OffX
) ) 1 2 exp ( - ( 2 n + 1 ) 2 4 B ( t - OffX ) ) + OffY ( 34 )
##EQU00032##
[0212] The values of OffX and OffY considered in the estimation of
the background noise can be decorrelated from those considered in
the estimation of the permeation.
[0213] The algorithm of an offset correction of the estimation of
the background noise and/or the permeation can correspond to:
TABLE-US-00001 for a ranging from -Y.sub.1 to Y.sub.1 per pitch of
1.10.sup.-15, for b ranging from -X.sub.1 to X.sub.1 per pitch of
1, Determine the estimation J.sub.estim(t) having the minimum error
with the measurement signal J.sub.measurement modified by the
offset a on the ordinate axis and by the offset b on the abscise
axis, if the global error < recorded global error, then recorded
global error = global error, OffY = a OffX = b End if End for End
for
[0214] In this algorithm, Y.sub.1 can correspond to about one tenth
of the expected amplitude of the expected signal J.sub.measurement,
and X.sub.1 can correspond to about one third of the expected
duration of the measurement.
[0215] The estimation giving the lowest global error is then
obtained by using OffY and OffX as offsets on the ordinate and
abscissa axes.
[0216] This offset calculation can in particular be implemented for
each permeation regimen calculated when the gas flow is estimated
as corresponding to a combination of several permeation
regimens.
[0217] In the previously described examples, the Fick laws are used
as models for predicting the change over time of the background
noise and gas flow through the barrier layer 10. Alternatively, it
is possible to correlate the change over time of the background
noise and gas flow to data, that is curves, for example obtained by
learning or corresponding to a library provided, for example stored
in a learning database. Each of these curves is for example
associated with values of the parameters A and B or possibly
directly to values of the parameters J.infin. and TL. At each
iteration of the method implemented to improve the correspondence
between the measurement and the estimation (the estimation of the
gas flow J.sub.perm.sub.--.sub.estim(t) corresponds in this case to
one of the curves of the database), the estimation error is reduced
between the measurement and the estimation by choosing the curve
which best corresponds to the measurements carried out. Finally,
the curve of the database which best corresponds to the
measurements (background noise and/or gas flow) carried out is
chosen as that corresponding to the permeation model of the barrier
layer 10.
[0218] The values of A and B of the chosen curve can then be
considered as corresponding to those of the barrier layer 10, and
from which it is possible to calculate the parameters J.infin. and
TL to estimate the permeation of the barrier layer 10. In the same
way, several curves can be chosen in the case of a permeation
governed by several permeation regimens.
[0219] In the previously described embodiment, first an estimation
of the change over time of the background noise is made, and then
the parameters A and B are estimated via the estimation of the
change over time of the gas flow through the barrier layer 10,
these estimated parameters A and B being then used to estimate the
permeation of the barrier layer 10 via the calculation of J.infin.
and possibly of TL. Alternatively, it is possible to take both
parameters A and B into account, called for example A.sub.degas and
B.sub.degas, estimated during the estimation of the background
noise to calculate a first stabilized transfer rate, and the
parameters A and B, called for example A.sub.perm and B.sub.perm,
estimated during the estimation of the change over time of the gas
flow to calculate a second stabilized transfer rate.
[0220] In another embodiment, the method for estimating the
permeation of the barrier layer 10 can consist in implementing
steps 102.1 to 102.7 as previously described in order to obtain an
estimation of the values of the parameters A and B via the
estimation of the change over time of the background noise. From
these values A and B, it is possible to directly calculate J.infin.
and possibly TL in order to estimate the permeation of the barrier
layer 10, without implementing steps 104 to 108. This other
embodiment is preferably implemented in the case of a barrier layer
saturated with target gases. In this case, the first chamber 12 is
for example nonexistent or the access between the first and second
chambers is sealingly blocked, in order to avoid a desorption of
the barrier layer off the second chamber. When several degassing
regimens are taken into consideration, it is possible to calculate
a value of a stabilized flow J.infin. and of TL for each degassing
regimen identified.
[0221] In another embodiment, the method for estimating the
permeation of the barrier layer 10 can consist in implementing
steps 104 to 108 as previously described without implementing step
102 beforehand, that is without making an estimation of the change
over time of the background noise. In this case, the background
noise is not subtracted from the measurement of the gas flow
through the barrier layer 10 made. Although less accurate and
having a lesser measurement sensitivity than when the background
noise is taken into consideration, such an embodiment has however
the advantage of being quick and suitable for a great number of
barrier layers.
[0222] Whatever the embodiment considered, when several permeation
regimens and/or several degassing regimens are considered, it is
possible to make the calculation of a stabilized gas flow
J.infin..sub.1 such that J.infin..sub.1=A.sub.1B.sub.1 and/or the
calculation of stabilized gas flows J.infin..sub.X such that
J .infin. X = i = 1 X A i B i ##EQU00033##
where X represents the number of the regimen the permeation of
which is desired to be known, in the case of several permeation
regimens which are added up.
[0223] The method for estimating the permeation of the barrier
layer 10 can be implemented by a device 200 for estimating a
permeation as shown for example in FIG. 12. The device 200 includes
the previously described permeameter 11, as well as one or more
computers 202, or calculation units, able to form an input/output
interface with the operator. The computer(s) 202 are connected to
the permeameter 11 in order in particular to drive the permeameter
11, receive the measurement signals delivered by the measuring
device 16 of the permeameter 11, making all the calculations of the
method, etc.
* * * * *